The Early Exercise Risk Premium

We study the asset pricing implications of being able to optimally early exercise plain vanilla puts, contrasting expected raw and delta-hedged returns across equivalent American and European puts. Our theory suggests that American puts yield less negative raw but more negative delta-hedged expected returns than equivalent European puts. The raw (delta-hedged) spread widens with a higher early exercise probability as induced through, for example, moneyness, time to maturity, and underlying asset volatility (variance and jump risk premiums). An empirical comparison of single-stock American puts with equivalent synthetic European puts formed from put–call parity supports our theory if and only if we allow for optimal early exercises in our return calculations. More strikingly, allowing for optimal early exercises significantly alters the profitability of 14 out of 15 well-known option anomalies with the average absolute change equal to 33% and five anomalies becoming insignificant.